NC = Bass boost, heh.
These effects are inherently 'coupled'.
The noise cancelling works by comparing sounds on the outside of the cup to those within the cup.
It thus has 2 microphones (which is what makes the NC so noisy in most cases).
The headphone also has to know which signal should be in the cups and that is the audio signal.
Because of this the NC also compares the signal the driver reproduces against that from the mic inside the cups.
If the driver/earpad combo is rolled off the mic inside will try to compensate the bass levels 'flat'.
This is why with NC on you generally see a better LF extension/flatness.
The difference between 2 mics only works for lower frequencies because of acoustic wavelength/delay which needs to be much bigger than the relative sizes inside the cups.
For this reason the BW in which NC works is limited to the upper mids at best so you don't see/hear much effects in the highs, although it might appear that way due to the masking by the increased lower frequencies.
The increase in 'distortion' with NC on is most likely caused by noise (mic pre-amps) and things the microphones pick up rather than THD of the amplifier section in the headphone itself.
Think of the 'bass correction' as Philips Motional FeedBack, although that was done inside the woofer with a X'tal 'pickup' instead of a mic insde the cabinet.
